# Universality class of the percolation in two-dimensional lattices with distortion

## TL;DR

This study reexamines a distorted lattice percolation model and confirms that it shares the same universality class as classical two-dimensional percolation through high-precision analysis of critical exponents.

## Contribution

The paper provides high-precision numerical evidence that percolation in distorted lattices belongs to the classical universality class, clarifying previous inconsistent results.

## Key findings

- Critical exponents match those of classical percolation within error bars.
- Percolation thresholds are accurately determined for various lattices.
- Distorted lattices do not form a new universality class.

## Abstract

Mitra et al. [Phys. Rev. E 99 (2019) 012117] proposed a new percolation model that includes distortion in the square lattice and concluded that it may belong to the same universality class as the ordinary percolation. But the conclusion is questionable since their results of critical exponents are not consistent. In this paper, we reexamined the new model with high precision in the square, triangular, and honeycomb lattices by using the Newman-Ziff algorithm. Through the finite-size scaling, we obtained the percolation threshold of the infinite-size lattice and critical exponents ($\nu$ and $\beta$). Our results of the critical exponents are the same as those of the classical percolation within error bars, and the percolation in distorted lattices is confirmed to belong to the universality class of the classical percolation in two dimensions.